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Nataly [62]
3 years ago
13

1.Why is it more important to interact with your instructors in college than it was in high school?

Advanced Placement (AP)
1 answer:
Arlecino [84]3 years ago
3 0

Answer:

In college, your professors rarely reach out to you. High school educators often take more initiative, and would often check in with you if they notice something off. In college, you're expected to take that initiative and actively network with your professors.

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Explain in detail, how you solved the following problem: The first two terms of a sequence are 10 and 20. If each term after the
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Answer:

T_{2020} = 15

Explanation:

Given

T_1 = 10

T_2 = 20

Each term after the second term is the average of all of the preceding terms

Required:

Explain how to solve the 2020th term

Solve the 2020th term

Solving the 2020th term of a sequence using conventional method may be a little bit difficult but in questions like this, it's not.

The very first thing to do is to solve for the third term;

The value of the third term is the value of every other term after the second term of the sequence; So, what I'll do is that I'll assign the value of the third term to the 2020th term

<em>This is proved as follows;</em>

From the question, we have that "..... each term after the second term is the average of all of the preceding terms", in other words the MEAN

T_{n} = \frac{\sum T{k}}{n-1} ; where: k = 1 .... n -1

<em>Assume n = 3</em>

T_{3} = \frac{T_1 + T_2}{2}

<em>Multiply both sides by 2</em>

2 * T_{3} = \frac{T_1 + T_2}{2} * 2

2T_{3} = T_1 + T_2

<em>Assume n = 4</em>

T_{4} = \frac{T_1 + T_2 + T_3}{3}

T_{4} = \frac{(T_1 + T_2) + T_3}{3}

Substitute 2T_{3} = T_1 + T_2

T_{4} = \frac{2T_3 + T_3}{3}

T_{4} = \frac{3T_3}{3}

T_{4} = T_3

Assume n = 5

T_{5} = \frac{T_1 + T_2 + T_3 +T_4}{4}

T_{5} = \frac{(T_1 + T_2) + T_3 +(T_4)}{4}

Substitute 2T_{3} = T_1 + T_2 and T_{4} = T_3

T_{5} = \frac{2T_3 + T_3 +T_3}{4}

T_{5} = \frac{4T_3}{4}

T_{5} = \frac{(5-1)T_3}{5-1}

<em>Replace 5 with n</em>

T_{n} = \frac{(n-1)T_3}{n-1}

<em>(n-1) will definitely cancel out (n-1); So, we're left with</em>

T_{n} = T_3

Hence,

T_{2020} = T_3

Calculating T_3

T_{3} = \frac{10 + 20}{2}

T_{3} = \frac{30}{2}

T_{3} = 15

Recall that T_{2020} = T_3

T_{2020} = 15

3 0
3 years ago
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